相关论文: Compact Quantum Groupoids

To any complex Hadamard matrix we associate a quantum permutation group. The correspondence is not one-to-one, but the quantum group encapsulates a number of subtle properties of the matrix. We investigate various aspects of the…

We prove the existence of a quantum isometry groups for new classes of metric spaces: (i) geodesic metrics for compact connected Riemannian manifolds (possibly with boundary) and (ii) metric spaces admitting a uniformly distributed…

We show how to construct a compact quantum metric space from a proper continuous length function on an \'etale groupoid with compact unit space, where the unit space additionally has the structure of a compact metric space. Using compactly…

A braided generalization of the concept of Hopf algebra (quantum group) is presented. The generalization overcomes an inherent geometrical inhomogeneity of quantum groups, in the sense of allowing completely pointless objects. All…

Generalizing the notion of continuous Hilbert space representations of compact topological groups we define unitary continuous correpresentations of $C^*$-completions of compact quantum group Hopf algebras on arbitrary Hilbert spaces. It is…

We consider a twisted version of quantum groups corepresentations. This generalization amounts to include in the theory the case where quantum space coordinates and its endomorphism matrix entries belong to a non-commutative quadratic…

In this short letter we review Schwinger's formulation of Quantum Mechanics and we argue that the mathematical structure behind Schwinger's "Symbolism of Atomic Measurements" is that of a groupoid. In this framework, both the Hilbert space…

We define and study an analogue of the Baum-Connes assembly map for complex semisimple quantum groups, that is, Drinfeld doubles of $ q $-deformations of compact semisimple Lie groups. Our starting point is the deformation picture of the…

Topological quivers generalize the notion of directed graphs in which the sets of vertices and edges are locally compact (second countable) Hausdorff spaces. Associated to a topological quiver $Q$ is a $C^*$-correspondence, and in turn, a…

We study glued tensor and free products of compact matrix quantum groups with cyclic groups -- so-called tensor and free complexifications. We characterize them by studying their representation categories and algebraic relations. In…

Let $\Uq$ be a quantum group. Regarding a (noncommutative) space with $\Uq$-symmetry as a $\Uq$-module algebra $A$, we may think of equivariant vector bundles on $A$ as projective $A$-modules with compatible $\Uq$-action. We construct an…

In this work, we introduce a class of Timmermann's measured multiplier Hopf *-algebroids called algebraic quantum transformation groupoids of compact type. Each object in this class admits a Pontrjagin-like dual called an algebraic quantum…

Symmetry groups are projectively represented in quantum mechanics, and crystalline symmetries are fundamental in condensed matter physics. Here, we systematically present a unified theory of quantum mechanical space groups from two…

In this paper we associate to every reduced C*-algebraic quantum group A a universal C*-algebraic quantum group. We fine tune a proof of Kirchberg to show that every *-representation of a modified L1-space is generated by a unitary…

The categories of representations of compact quantum groups of automorphisms of certain inclusions of finite dimensional C*-algebras are shown to be isomorphic to the categories of Fuss-Catalan diagrams.

A group-category is an additively semisimple category with a monoidal product structure in which the simple objects are invertible. For example in the category of representations of a group, 1-dimensional representations are the invertible…

In this paper, we give a construction of a (C*-algebraic) quantum Heisenberg group. This is done by viewing it as the dual quantum group of the specific non-compact quantum group (A,\Delta) constructed earlier by the author. Our definition…

In this paper we discuss generalized group, provides some interesting examples. Further we introduce a generalized module as a module like structure obtained from a generalized group and discuss some of its properties and we also describes…

We introduce the notion of locally trivial quantum principal bundles. The base space and total space are compact quantum spaces (unital $C^{\star}$-algebras), the structure group is a compact matrix quantum group. We prove that a quantum…

In this paper, we quantize universal gauge groups such as SU(\infty), in the sigma-C*-algebra setting. More precisely, we propose a concise definition of sigma-C*-quantum groups and explain the concept here. At the same time, we put this…